Abstract

We obtain a representation for the norm of certain compact weighted
composition operator 𝐶𝜓,𝜑 on the Hardy space 𝐻2, whenever 𝜑(𝑧)=𝑎𝑧+𝑏 and 𝜓(𝑧)=𝑎𝑧−𝑏. We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on 𝜑 and 𝜓. Moreover, we characterize the norm and essential norm of such operators in a special case.